IDEAS home Printed from https://ideas.repec.org/p/bro/econwp/2008-8.html
   My bibliography  Save this paper

Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World

Author

Listed:

Abstract

In this paper we provide two simple new versions of Arrow’s impossibility theorem, in a model with only one preference profile. Both versions are transparent, requiring minimal mathematical sophistication. The first version assumes there are only two people in society, whose preferences are being aggregated; the second version assumes two or more people. Both theorems rely on assumptions about diversity of preferences, and we explore alternative notions of diversity at some length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to illustrate our points.

Suggested Citation

  • Allan M Feldman & Roberto Serrano, 2008. "Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers 2008-8, Brown University, Department of Economics.
  • Handle: RePEc:bro:econwp:2008-8
    as

    Download full text from publisher

    File URL: http://www.brown.edu/academics/economics/sites/brown.edu.academics.economics/files/uploads/2008-8_paper.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Robert P. Parks, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 447-450.
    2. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328-328.
    3. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    4. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
    5. Abram Burk, 1938. "A Reformulation of Certain Aspects of Welfare Economics," The Quarterly Journal of Economics, Oxford University Press, vol. 52(2), pages 310-334.
    6. Robert A. Pollak, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 73-90.
    7. Kevin W. S. Roberts, 1980. "Social Choice Theory: The Single-profile and Multi-profile Approaches," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 441-450.
    8. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    9. Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 381-418, December.
    10. Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
    11. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Arrow's Theorem; single-profile;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bro:econwp:2008-8. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Brown Economics Webmaster). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.